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The evolution of ft is governed by four parameters: σΔa, μm, σm, and ρm (see equations [6] and [7]). Table 2a summarizes the posterior for these parameters. The posterior median for σΔa is somewhat lower than a typical estimate for the United States, but this is consistent with using the OECD average for ft. The spread of the posterior is roughly what one would find using 16 i.i.d. normal observations, that is, using q=16 low-frequency observations with Δft an i.i.d. process. The posterior for the average growth rate, μm, is centered around 1.9% per year with 67% error bands of roughly ±1% per year. Figure 3b shows the posterior estimates for mt, the local level of Δft. The posterior median shows some variation over the sample, but a constant value of 1.9% (its mean) is within the (pointwise) 67% credible set for all dates.

Table 2.

Posterior Percentiles

a. Posterior percentiles for selected parameters, ft and ct processes
Percentiles of Posterior
Parameter0.050.170.500.840.95
i. Parameters for ft process (in percentage points) 
σΔa 2.34 2.70 3.33 4.14 4.87 
μm −0.08 0.77 1.85 2.79 3.56 
σm 0.42 0.73 1.13 1.52 1.76 
hm 50 63 96 133 146 
ii. Parameters for c process 
μc −0.97 −0.83 −0.63 −0.45 −0.32 
a. Posterior percentiles for selected parameters, ft and ct processes
Percentiles of Posterior
Parameter0.050.170.500.840.95
i. Parameters for ft process (in percentage points) 
σΔa 2.34 2.70 3.33 4.14 4.87 
μm −0.08 0.77 1.85 2.79 3.56 
σm 0.42 0.73 1.13 1.52 1.76 
hm 50 63 96 133 146 
ii. Parameters for c process 
μc −0.97 −0.83 −0.63 −0.45 −0.32 

Δft=mt+Δat, where Δat is I(0) and mt is a low-frequency AR(1) with mean μm and low-frequency AR coefficient ρm. The half-life, hm, solves ρmhm=1/2.

b. Posterior percentiles for selected parameters, ci,t process
Half-lifeσcσ(ct+50-ct)
Percentiles of Posterior
0.170.500.840.170.500.840.170.500.84
i. Pooled across countries 
All countries 130 233 389 0.85 1.10 1.37 0.45 0.63 0.86 
OECD 201 338 486 0.74 0.91 1.15 0.35 0.44 0.58 
Non-OECD 121 211 342 0.91 1.15 1.40 0.52 0.68 0.89 
ii. Selected countries 
China 150 222 330 1.00 1.20 1.40 0.59 0.68 0.79 
Singapore 111 185 291 0.92 1.13 1.34 0.61 0.72 0.86 
Madagascar 148 214 317 1.08 1.24 1.42 0.61 0.72 0.85 
Belgium 286 394 507 0.69 0.82 0.98 0.32 0.37 0.44 
Russia 78 138 239 0.90 1.10 1.34 0.66 0.79 0.94 
United States 303 413 529 0.75 0.89 1.06 0.34 0.39 0.45 
Australia 340 461 567 0.71 0.84 1.00 0.30 0.34 0.40 
Liberia 50 70 108 1.36 1.51 1.62 1.17 1.34 1.50 
b. Posterior percentiles for selected parameters, ci,t process
Half-lifeσcσ(ct+50-ct)
Percentiles of Posterior
0.170.500.840.170.500.840.170.500.84
i. Pooled across countries 
All countries 130 233 389 0.85 1.10 1.37 0.45 0.63 0.86 
OECD 201 338 486 0.74 0.91 1.15 0.35 0.44 0.58 
Non-OECD 121 211 342 0.91 1.15 1.40 0.52 0.68 0.89 
ii. Selected countries 
China 150 222 330 1.00 1.20 1.40 0.59 0.68 0.79 
Singapore 111 185 291 0.92 1.13 1.34 0.61 0.72 0.86 
Madagascar 148 214 317 1.08 1.24 1.42 0.61 0.72 0.85 
Belgium 286 394 507 0.69 0.82 0.98 0.32 0.37 0.44 
Russia 78 138 239 0.90 1.10 1.34 0.66 0.79 0.94 
United States 303 413 529 0.75 0.89 1.06 0.34 0.39 0.45 
Australia 340 461 567 0.71 0.84 1.00 0.30 0.34 0.40 
Liberia 50 70 108 1.36 1.51 1.62 1.17 1.34 1.50 

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